Nowadays, application of laser is deeply engaged in every aspect of the modern life of human beings. In the application of laser, various applied optical systems required for meeting the demands of various processes are indispensable. Presently, the laser marking machine existing in the market are gradually replacing various ink writers, screen printers and the like due to the characteristics of its fast speed, great flexibility, needing no consumables, permanent marking and so on.
The F-theta (fθ) lens is a kind of photographic objective lens that has a large field of view, medium and small-sized aperture, and medium and long-sized focal length. Choosing a photographic objective lens of a “three-piece” type will be relatively suitable concerning the parameters it is to possess. The flat-field optical lens for laser scanning is called fθ lens, and this lens achieves that, when the laser beam is scanning at a constant angular velocity, focusing point of the light beam transmitting through this lens on the image plane is also moving at a uniform speed, which determines that scanning angle of the light beam and image height of the focusing point on the image plane will establish a linear relationship. A galvanometer laser marking machine is realized due to the present of the fθ lens.
FIG. 1 is a typical fθ lens optical system in the conventional art, in which the light beam is reflected by a reflector that is scanning at an angular velocity rotating at uniform speed, then focused on the image plane by the fθ lens, that is, the light beam sequentially passes two galvanometers 1 and 2 that are respectively rotating about the x-axis and the y-axis, and at last passes through the fθ lens 3 and is focused on the image plane 4, so as to form an image by scanning with the galvanometer. The fθ lens 3 is a flat-field focusing lens. It is required that image height η on the image plane has a linear relationship with the scanning angle θ of the X galvanometer 1 and the Y galvanometer 2 upon marking, that is, η=f*θ(Sr), wherein, assuming that incident angle of light with respect to the fθ lens at a certain point of time is θ, the image height of the generated image with respect to the center point is then there must exist a linear relationship therebetween, that is, η=k*f*θ. Wherein, k is a constant; f is the focal length of the fθ lens, which is a fixed value for a particular lens; and θ is the scanning angle of the galvanometer (in radians).
According to the theory of Gauss optical imaging, it is known that the image height η has a following relationship with the focal length f of the lens and the angle of rotation θ of the light beam: η=f*tgθ. However, normally, there is always a certain distortion in an imaging system. Assuming that in the correction of aberration of the optical design, a distortion Δη is intentionally introduced in, so as to satisfy the relationship as shown in the formula below: η=f*tgθ−Δ η=k*f*θ, then the requirement that the object-image relationship of the fθ lens is a linear relationship may be achieved. Therefore, it is derived that Δη=f*tgθ−k*f*θ=f(tgθ−k*θ), wherein Δη is a positive value, and the fθ lens is an optical system with a negative distortion. Therefore, it is required that the system has a relatively large negative distortion when the angle is relatively large.
Meanwhile, the diaphragm of the fθ lens which is outside of the lens is a typical non-symmetrical optical system. When issue of the balance of the vertical aberration is concerned in the design of the existing products, generally, the design is carried out by adopting the symmetrical structure of Pitzval, so as to achieve the correction of the vertical aberration. However, on the contrary, it is very difficult to correct the vertical aberration very well by adopting the symmetrical structure of Pitzval to design this kind of non-symmetrical optical system.
In addition, another feature of the fθ lens is to require that all the focus points within the range of imaging must have a similar quality of focusing and no vignetting is allowed, so as to assure that all the image points are consistent. In order to increase the service life of the lens, it is required to adopt no cemented lens when it is used in a laser applied light path due to very large energy density of the laser sometimes.